WEBVTT
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If π₯ and π¦ are two variables such that the summation of π₯ equals 15, the summation of π¦ equals 25, the summation of π₯ times π¦ equals 75, and π equals five, find the linear correlation coefficient, π, between π₯ and π¦.
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What do we know about the linear correlation coefficient?
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And this coefficient, π, can be found by multiplying π times the summation of π₯ times π¦ minus the summation of π₯ times the summation of π¦.
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All over the square root of π times the summation of π₯ squared minus the summation of π₯ squared times π times the summation of π¦ squared minus the summation of π¦ squared.
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And while itβs a long formula, in this case, thereβs something we can notice.
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Our π equals five.
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And the summation of π₯ times π¦ equals 75.
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We need to subtract that from 15 times 25.
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This will all be over the square root of some value in the denominator.
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However, letβs examine the numerator a little bit more closely.
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I can rewrite 75 as three times 25.
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Five times 75 equals five times three times 25.
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If we regroup one more time, five times three equals 15.
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We rewrite five times 75 as 15 times 25.
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And then we see that our numerator is 15 times 25 minus 15 times 25.
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Our numerator equals zero.
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And that means the linear correlation coefficient, π, equals zero over some value.
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And we donβt need to know whatβs in the denominator.
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π equals zero.